An object acted on by a single, linear restoring force will undergo simple harmo

Question

An object acted on by a single, linear restoring force will undergo simple harmonic motion. For simple harmonic motion, if an object is at its maximum position at time t=0s, the position and velocity at a later time (t) can be written as

x=Acos(t) v=-Asin(t)

where A is the amplitude of the oscillation.

Now, assume the object from part a) is at x=0.5m at t=0s and is released.

Using your previous results for , determine the position and velocity of the mass as a function of time, fill in the table on the left, and graph the results.

From the graph of position versus time, does the period agree with the result from part a)? Is it the same as the period of the velocity as a function of time?

1) Approximately, what is the maximum speed of the mass and where does the maximum speed occur in
relation to the position?

2) What is the minimum speed of the mass and where does the minimum speed occur in relation to the position?

3) Input functions(f) into cells D2 and E2 (Assume A2 is 3.16)

Explanation / Answer

From the fragment of spreadsheet you show, it looks like is 3.16 s-1.

Assuming that's true,

(a) maximum speed is when x=0 (as the particle crosses the axis) and is A = 1.58 m/s (we see from the spreadsheet that A = 0.5 m)

(b) minimum speed is of course zero, and ccurs whenever the particle reaches its maximum amplitude: x = 0.5 or x = -0.5

(c) not sure what you want here; the excel formula for x and v is something like:

x: =B$2*cos(A$2*C$2)

v: =-A$2*B$2*sin(A$2*C$2)

you can take the dollar signs out if you want, they make the references relative so the formula can be copied down the sheet

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